login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A286185 Number of connected induced (non-null) subgraphs of the Möbius ladder graph with 2n nodes. 15
3, 15, 55, 173, 511, 1451, 4019, 10937, 29371, 78055, 205679, 538149, 1399607, 3621315, 9327723, 23931633, 61186163, 155949119, 396369831, 1004904733, 2541896559, 6416348251, 16165611043, 40657256617, 102090514731, 255968753175, 640899345631, 1602640560533 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Möbius Ladder

Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph

FORMULA

a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 5*a(n-4) - 2*a(n-5) - a(n-6), for n>6 (conjectured).

a(n) = 1/4*((1-sqrt(2))^n*(4-3*sqrt(2)*n) + (1+sqrt(2))^n*(4+3*sqrt(2)*n)) - 1 - n (conjectured). - Eric W. Weisstein, May 08 2017

a(n) = Lucas(n, 2) + 3*n*Fibonacci(n, 2) - n - 1, where Lucas(n, 2) = A002203(n) and Fibonacci(n, 2) = A000129(n) (conjectured). - Eric W. Weisstein, May 08 2017

G.f. (subject to the above conjectures. In fact all three conjectures are equivalent): (3*x-3*x^2-2*x^3-4*x^4+3*x^5-x^6)/(1-3*x+x^2+x^3)^2. - Robert Israel, May 08 2017

MATHEMATICA

a[n_] := Block[{g = CirculantGraph[2 n, {1, n}]}, -1 + ParallelSum[ Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[2 n]}]]; Array[a, 8]

CROSSREFS

Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286186 (friendship), A286187 (web), A286188 (gear), A286189 (rook), A285765 (queen).

Sequence in context: A117960 A176288 A119113 * A152896 A007973 A261737

Adjacent sequences:  A286182 A286183 A286184 * A286186 A286187 A286188

KEYWORD

nonn

AUTHOR

Giovanni Resta, May 04 2017

EXTENSIONS

a(17)-a(28) from Andrew Howroyd, May 20 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 24 18:12 EDT 2019. Contains 326295 sequences. (Running on oeis4.)